Reducing the ambiguity of Parikh matrices

The Parikh matrix mapping allows us to describe words using matrices. Whilst compact, this description comes with a level of ambiguity since a single matrix may describe multiple words. In this paper, we investigate how considering the Parikh matrices of various transformations of a given word can decrease that ambiguity. More specifically, for any word, we study the Parikh matrix of its projection to a smaller alphabet as well as that of its Lyndon conjugate. Our results demonstrate that ambiguity can often be reduced using these concepts, and we give conditions on when they succeed. (C) 2021 Elsevier B.V. All rights reserved.